Figure 4
From: Ferroelectricity driven magnetism at domain walls in LaAlO3/PbTiO3 superlattices

Distribution of (dPiz/dz,Mi2) points in all above pure GGA calculations.
For each case of a given SL, Piz of Ti is first fitted by a polynomial function of z. Here, i is the unit layer number. Then the value of dPiz/dz is derived analytically. This process can reduce the inaccuracy due to a few discrete points as much as possible. The broken curve is just for a guide of eyes.